Feedback equation
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Aidan135711
diyAudio Member

Join Date: Feb 2008
Feedback equation

Does anybody know an equation to calculate the effect on gain of the negative feedback resistor in in the diagram below?
I know about the universal feedback equation,can I use it and if so,is the feedback fraction still Rk/RL?
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Miles Prower
diyAudio Member

Join Date: May 2005
Location: USA
Re: Feedback equation

Quote:
 Originally posted by Aidan135711 I know about the universal feedback equation,can I use it and if so,is the feedback fraction still Rk/RL?
No, and it never was. The Rk/Rl simplification works for BJTs since these are high gain devices, much higher gain than any VT. To solve that circuit, you need to determine the open loop gain with the cathode degeneration from the loadlines. Then you figure the new gain obtained from adding the plate feedback from the usual feedback formula.

Of course, that brings up the question of why use a 12AX7 in that case? Between cathode degeneration and plate feedback, you're throwing off a lot of gain there. The closed loop gain will probably be in the same territory as using a 6SN7 anode follower running without cathode degeneration. The 6SN7 might be a better choice than a 12AX7 in that case.
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 14th January 2009, 07:23 PM #3 Aidan135711   diyAudio Member     Join Date: Feb 2008 Thanks for your reply. I have already calculated the open loop gain using loadlines and this checks out about the same when I calculate gain using; Av=uxRL/RL+ra where u is Mu. which is between 41 and 46 depending which method I used. I then used the universal feedback equation from Morgan Jones book"Valve Amplifiers" to calculate the effect of the cathode degeneration.He used the equation on page 77 for this purpose and he called it the universal feedback equation. Afbk=Ao/1+bxAo where b is the feedback fraction Rk/RL and this reduced the gain to about 21. So,what I need to know is how do I figure the new gain obtained from adding the plate feedback and what is this"usual formula"? I am a Techy but am new to tubes so forgive me if my post seems long winded.
 14th January 2009, 08:21 PM #4 Aidan135711   diyAudio Member     Join Date: Feb 2008 I just found the equation on Aikenamps website Acl = (Ro + A*Rf) / (Ri + Rf + Ro - Ri*A) where Ro = internal output resistance of the stage
Miles Prower
diyAudio Member

Join Date: May 2005
Location: USA
I tend to stay away from equations like that since factors like u are all over the place. I design from loadlines instead. Here, the loadline is quite a bit steeper than this type likes to see. The open loop THD estimate is pretty hideous. Of course, adding cathode degeneration will help fix that. Knowing the plate currents, and given a 1K2 cathode resistor, you can figure:

Vk(min)= (1.2)(0.11)= 0.13V (Vgk= -3.0V)
Vk(max)= (2.6)(1.2)= 3.12V (Vgk= 0V)

Vi(+)= 3.12V
Vi(-)= -2.87V
Vi= 3.12 + 2.87= 5.99Vp-p

Given the output voltages:

Av`= (245 - 120) / 5.99= 20.87

THD`= 10(3.0 / 5.99)= 5.0% (Barely acceptable)

You can also read off the approximate g(m) and u with a delta Vgk= 1.0V, and get the r(p) from that.

The Aiken amps equation can then be used, and will be a good deal more accurate than the simplified one that works for op-amps since it takes into account a much lower open loop gain.

You also have to watch out for unexpected results since that feedback resistor is in series with whatever impedance the input has (it'll change tremendously with a volume control up front).
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 15th January 2009, 10:37 PM #6 Aidan135711   diyAudio Member     Join Date: Feb 2008 Hey Miles,thanks for the information. It seems there are many ways of calculating this stuff.We have used different methods but come up with almost the same answers. On the GRAPH you had an Av of 41.67 which is almost what I got as the open loop gain without taking into account cathode degeneration.I got 21 after factoring this in. In your POST you had an Av of 20.87 so I assume that your calculations in the post somehow already factor in cathode degeneration. I have 2 questions for you if you dont mind. 1. Where did you get this bit from? Vi(+)= 3.12V Vi(-)= -2.87V Vi= 3.12 + 2.87= 5.99Vp-p 2. I used the "Aiken Amps" equation where the gain(Ao) I used was 41 and got an answer of 4 which I know is right because the schematic shows 1.32v going into the input resistor and 4.2v at the output.This gives an Av of about 3.1 but I think the level after the input resistor is about 1v so a gain of about 4 seems right. It seems the Aiken equation somehow included cathode degeneration too.What do you think? By the way,this is an old Hammond organ amp.I might modify it to be a guitar amp or gut it and just build a Marshall 18W into it.In the meantime I am studying it to try and learn hence my silly questions.
 15th January 2009, 10:58 PM #7 wakibaki   Banned   Join Date: Jan 2008 An old Hammond organ amp might be worth preserving as a heritage item. Just a thought. I don't know, but if I was an old Hammond organ player I might want one of those... You can easy get a chassis to build the Marshall, and in some ways it's better to start with all new components. w
 15th January 2009, 11:06 PM #8 Aidan135711   diyAudio Member     Join Date: Feb 2008 The organ was destroyed on a bonfire.The amp/psu chassis and the Jensen P12S speaker is all that remains.It needed 2 new twistlock caps and an EZ81.Also had to get a reverb unit from accutronics for it.When very low level guitar is put through it ,it sounds nice but gets very dirty(not nice dirtyness) when guitar is turned up. It is called an AO-48 and came from an Everett 2000 (by Hammond)
 15th January 2009, 11:57 PM #9 Aidan135711   diyAudio Member     Join Date: Feb 2008 Miles I see now where you got this bit from Vi(+)= 3.12V Vi(-)= -2.87V Vi= 3.12 + 2.87= 5.99Vp-p and I also see it does include cathode degeneration.
Miles Prower
diyAudio Member

Join Date: May 2005
Location: USA
Quote:
 Originally posted by Aidan135711 2. I used the "Aiken Amps" equation where the gain(Ao) I used was 41 and got an answer of 4 which I know is right because the schematic shows 1.32v going into the input resistor and 4.2v at the output.This gives an Av of about 3.1 but I think the level after the input resistor is about 1v so a gain of about 4 seems right. It seems the Aiken equation somehow included cathode degeneration too.What do you think?
The Aiken equation does account for the possibility of cathode degeneration by including a figure for r(p) (Ro in that equation). With an unbypassed cathode resistor, the r(p) increases above what it would otherwise be. You don't see that effect so much with either pentodes or transistors. It is also why cascodes have such high effective r(p)'s.
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